pyrt.rayleigh_legendre

pyrt.rayleigh_legendre(n_layers, n_wavelengths)

Make the generic Legendre decomposition of the Rayleigh scattering phase function.

Parameters:

• n_layers (int) – The number of layers to make the phase function for.

• n_wavelengths (int) – The number of wavelengths to make

Returns:

3-dimensional array of the Legendre decomposition of the phase function with a shape of (3, n_layers, n_wavelengths).

Return type:

np.ndarray

Notes

Moment 0 is always 1 and moment 2 is always 0.5. The Rayleigh scattering phase function is given by

\[P(\theta) = \frac{3}{4} (1 + \cos^2(\theta)).\]

Since \(P_0(x) = 1\) and \(P_2(x) = \frac{3x^2 - 1}{2}\), \(P(\mu) = P_0(\mu) + 0.5 P_2(\mu)\).

Examples

Make the Rayleigh scattering phase function for a model with 15 layers and 5 wavelengths.

>>> import pyrt
>>> rayleigh_pf = pyrt.rayleigh_legendre(15, 5)
>>> rayleigh_pf.shape
(3, 15, 5)